214
Digital Electronics
Output 1
Output 2
0000
0011
0100
0101
0111
0010
0110
0111
1010
1011
1111
ABCD
0−00
0−10
−010
010−
0−11
01−1
011−
101−
−111
1−11
For each prime implicant, check marks are placed only in columns that pertain to the outputs checked
off for this prime implicant. For instance, 0-00 has only output 1 checked off. Therefore, the relevant
terms under output 1 will be checked off. The completed table is treated as a whole while marking
the required prime implicants to be considered for writing the minimized expressions. The minimized
expressions are as follows:
Y 1 = AACCD + AACCD + AABBC and Y 2 = BBCCD + AABBC + AACCD
Example 6.9
Using the Quine–McCluskey tabular method, find the minimum sum of products for ffAA BB CC DD =
1 2 3 9 12 13 14 +
0 7 10 15.
Solution
The different steps to finding the solution to the given problem are tabulated below. As we can see,
eight prime implicants have been identified. These prime implicants along with the inputs constitute
the prime implicant table. Remember that optional inputs are not considered while constructing the
prime implicant table:
A
B
C
D
A
B
C
D
A
B
C
D
0
0
0
0
0
0
0
−
0
0
−
−
*
0
0
−
0
1
1
−
−
*
0
0
0
1
0
0
−
1
0
0
1
0
−
0
0
1
*
0
0
1
−
0
0
1
1
−
0
1
0
*
1
0
0
1
1
0
1
0
0
−
1
1
*
1
1
0
0
1
−
0
1
*
1
−
1
0
*
0
1
1
1
1
1
0
−
1
1
0
1
1
1
−
0
1
1
1
0
−
1
1
1
*
1
1
1
1
1
1
−
1
1
1
1
−